Pulse-height analysis in scintillation counting

ABSTRACT

Coincident output pulses of a plurality of photomultipliers are selected for counting on the basis of relative amplitude as well as sum. Improvement in background and isotope resolution is obtained in liquid scintillation counting. Pulse-height analysis circuits incorporating the improvement are described.

United States Patent Inventor Barton 11. Laney Deerfield, Ill.

Appl. No. 792,717

Filed Jan. 21, 1969 Patented Dec. 7, 1971 Assignee Nuclear-ChicagoCorporation Des Plaines, Ill.

PULSE-HEIGHT ANALYSIS IN SCINTILLATION COUNTING [56] lReierences CitedUNITED STATES PATENTS 3,320,419 5/1967 Thomas et a1. 250/106 SC3,388,254 6/1968 Haller et al. t 250/7l.5 3,484,703 12/1969 Thieberger250/7 1.5

Primary ExaminerArchie R. Borchelt Attorneys- Leonard G. Nierman, WalterC. Ramm and Lowell C. Bergstedt ABSTRACT: Coincident output pulses of aplurality of photomultipliers are selected for counting on the basis ofrelative amplitude as well as sum. Improvement in background 31 Claims,21 Drawing Figs.

11.8. C1 250/71.5 R, 250/83.3 R Int. Cl GOlt l/20 Field of Search250/71.5, 106 SC, 83.3

MPT

X PG 2 50 fill/O FG l MPT 52v Y 4, l

and isotope resolution is obtained in liquid scintillation counting.Pulse-height analysis circuits incorporating the improvement aredescribed.

CO INC I DE NCE ATTN' DISC. LOGIC ATTN. DISC. LOGIC ATTN. DISC. LOGICPATENTEI] DEB 712m 3528187 saw 1 BF 5 LOWER UPPER N (COUN C' (COUNTS)T=CO|NC|DENCE THRESHOLD BACKGRUJN X-l-Y (SUM SIGNAL) X NOISEP(PROBABILITY) BARTON LA/VEV PATENTEUDEB 7l97l 3 2 ,1 7

SHEET N []F 5 DISCRIMINIATION I L GATE AND COUNTING I 79 CIRCUITSMINIMUM 8/ 82 22/ p1- LEVEL 80 I O COINCI'DENCE VARIABLE 74 MPT MINIMUKMLEVEL VARIABLE MPT THRESHOLD x 86 DISCRIMINATOR L LEVEL SUM,-GATE.-DISCRIM CLIPPER V (80 INATOR I COINCIDENCE CIRCUIT CLIPPER 88 VARIABLETHRESHOLD 84/ DISCRIMINATOR l/Vl/E/VTUR BARTON H. LANE) PATENTEU DEC 7I971 SHEET 5 OF 5 0604 wozwoBzEo AIL 5 RIO/V h. LANE) PULSE-HEIGHTANALYSIS llN SCINTILLATKON COUNTING The present invention relates tomethods and apparatus for detection and measurement of low-level lightpulses, and particularly for the detection and measurement ofscintillations produced by beta-emissions in liquid scintillationcounting.

As is well known, the efficient counting of low-energy beta activitiesby liquid scintillation requires the counting of photomultiplier signalpulses of the same low order of amplitude as internally produced noisepulses. To discriminate against noise pulses, a plurality ofphotomultipliers, normally two, are used, and noncoincident pulses arerejected as attributable to noise. In basic coincidence counting, one ofthe multipliers is used solely as a coincidence tube for gating thetransmission of pulses from the other, which serves as the primarydetector or transducer whose output is employed in amplitude selection.Precision commercial liquid scintillation counting equipment alsoprovides for pulse summation," a symmetrical mode of operation in whichthe gains of the two tubes are balanced and the pulse outputs summed toform an overall output signal pulse, in addition to employing thecoincidence of the individual output pulses for gating the passing ofthe summed pulses. The summed signal has long been known to be moretruly representative of the amplitude of the light pulse producing thecoincident output pulses, particularly in the case of very weak pulses;however unsummed operation is sometimes preferred for certainmeasurements.

Amplitude analysis of the coincidence-gated signal pulses is normallyperformed by employment of lower-level and upperlevel discriminatorsconnected in anticoincidence to count only the pulses of amplitudeswithin the window thus fonned. Controls for selecting thesediscriminator levels, and also the minimum level of the output of eachtube required to form an accepted coincidence, are provided forselection by the user of desired values. Thus in the summation systemsheretofore known, the criteria for acceptance of a pulse for countingare (a) the amplitude of each of the coincident pulses must exceed apreselected fixed threshold value and (b) the sum of the amplitudes mustlie between preselected fixed minimum and maximum values (the minimumvalue criterion being essentially eliminated as a separate factor ofrejection where it is set at such a low value that it excludes nothingpassed by the coincidence system). In unsummed operation the criteriaare the same except that criterion (b) is applied to the output of onlyone tube, the coincidence tube frequently being run at higher gain forsuch operation.

The use of these criteria in liquid scintillation pulse-height analysishas been conventional for many years, and has, prior to the presentinvention, been accepted as producing the best possible discriminationbetween signal and noise in low-energy liquid scintillation counting,although residual noise pulses necessarily remain. By raising theminimum level of amplitude which is accepted as forming a coincidence,the noise background existing in any window" is reduced, but suchreduction is accompanied by a reduction in the counting efficiency forweak scintillations. Much efiort has been devoted to improvement ofphotomultipliers as regards noise reduction, and the better liquidscintillation systems normally incorporate provisions for refrigerationand other precautions designed to minimize photomultiplier noise. Theindex or figure of merit of a liquid scintillation system in thecounting of a low-energy isotope is normally taken as the factor EIB,where E is the efficiency and B is the background, although the indexE/B, the mere ratio of efficiency to background, is sometimes used. Truebackground due to cosmic rays, natural radiation from materials ofconstruction, etc., is normally minimized by appropriate shielding,selection of materials for minimum inherent radiation, and similarprecautions. Such sources of background have long since been reduced inhighsensitivity commercial equipment to the point where residual noisepulses constitute the primary source of counting background formeasurements on low-energy isotopes.

The present invention may be summarily described as lying in the findingthat the pulse analysis systems of the type long in universal useneglect information content of the individual multiplier outputamplitudes which is highly useful, particularly in rejecting many morenoise pulses without correspondingly afiecting counting efficiency,notably in the case of carbon -l4. (As later discussed the informationis also useful in distinguishing, on a statistical probability basis,between isotopes in plural-isotope counting, and additionally in reducing the scintillation background produced by true background radiation.)The present invention may be viewed either as the addition of furthercriteria to those mentioned as (a) and (b) above, or as adding aninterdependency between these criteria of acceptance, heretoforeindependent.

In one basic form of the invention, noise-pulse pairs exactly simulatingsignal-pulse pairs with the methods and apparatus of analysis ordiscrimination heretofore used are segregated from signal-pulse pairswith substantially high statistical reliability by employing therelative amplitudes of the coincident pulses as an additional criterion.The relative size of the individual pulses of noise coincidences isfound to have an entirely different probability distribution than therelative size of true scintillation pulses producing the same summedamplitude.

For coincident pulses of any given sum, the contributions of therespective tubes to that sum are not constant in all occurrences, butare statistically distributed, both in any large sam ple of signalpulses. and in any large sample of noise pulses. However, true signalpulses of all but the very smallest summed amplitude have a probabilityfunction or curve which has a single maximum substantially at pulseequality (with the matched multipliers and operating conditions of asummation system), since the basic mechanism of pulse-productioninvolves a generally equal division of the light energy of thescintillation between the two tubes, the variations from exact equalitybeing caused primarily by such factors as statistical fluctuations inphototube response, etc., the relative magnitude of which is smallexcept when the light pulse is itself very weak. On the other hand,equal coincident noise pulses from the respective tubes are relativelyrare for all but the smallest aggregate amplitudes, the probabilitycurve in this case for pulses of any given substantial sum having maximaat great inequality of the coincident pulses; coincident pulses ofappreciable sum occur predominantly with a relatively large pulse fromone tube and a relatively small pulse from the other, due both to theshape of the noise-pulse-amplitude spectrum in each tube and tocoincidences which are not in fact merely coincidental, but are causedby inducement of a small response in one tube to light-emission producedin occurrence of a discharge noise pulse in the other. Thus by merelyrejecting pulse pairs of predetermined disparity, a substantial portionof noise background pulses heretofore counted along with signal pulsesof substantial amplitude can be eliminated without appreciable reductionin counting efficiency for true scintillation events and this may bedone easily by a simple addition to conventional sum-discriminationequipment to produce a signal corresponding to the absolute differencebetween the signals and feeding this signal to any conventional type ofamplitude-discriminator, the latter being connected in anticoincidencewith the conventional window to block counting of summed pulses ofexcessive differential.

Although the addition of such a simple maximum difference discriminator"controlling the: pulse transmission in a conventional pulse-sum analysissystem produces substantial improvement by selection of proper limit ofdifferential empirically, still further improvement may be effected byrefinements of the basic principle resulting from study of the factorsdetermining the maximum differential between coincident pulses whichshould be permitted in accepting a sum-pulse as one to be counted. Anygiven limit of permitted differential will have a greater effect on theefficiency of counting large signal pulses than of small signal pulses,i.e., the probability that a true signal pulse of large amplitude willexceed a particular absolute differential in the contributions of thetwo tubes is substantially greater than the probability that a truesignal pulse of smaller sum amplitude will have such a differential ofthe contributions. Accordingly, the permitted differential should not beset the same for all energies of counted radiation. Where resetting of.the differential limit is objectionable, or where multiple radiationenergies are to be counted without introducing the complexity ofmultiple separate circuits, the simple differential criterion ofdiscrimination is advantageously replaced by one which has the pennittedlimits of difference between the contributions of the two tubes to anygiven sum an increasing function of the sum. For reasons later apparent,discrimination in which the permitted differential increases linearlywith the sum of the two individual coincident pulses may be called skewdifferential discrimination. When added to a conventional upper-andlowersum-discrimination system, a skew differential discriminator is capableof appreciable improvement in the ratio of efficiency (or its square) tobackground in the counting of a number of isotopes without resetting.

It will facilitate understanding of the invention, and of the furtherdiscussion, to point out more exactly the meaning of certain terms justused. In a conventional pulse-summation liquid scintillation system, itis a requirement for accepting pulses of any sum that each be of atleast the threshold coincidence value, which is the same for both tubesand the same for all sums. It will be seen that in a very broadtheoretical sense this in itself might be called a maximum-differentialdiscrimination system since the maximum permitted differential betweenindividual pulses of any given sum is the sum less twice the thresholdvalue, and the maximum permitted differential accordingly varies withthe sum by a relation which preserves a mere constant difference betweenany sum and the maximum permitted differential between the individualpulses producing that sum. The discussion of the present inventionherein will be understood to exclude such strained interpretation of theterminology employed, and the maximum permitted differential as hereindiscussed will be understood to refer to a maximum differential which isless, over at least a substantial portion of the range of permittedsums, than the sum minus the unvarying minimum individual pulsethreshold values of the prior art systems.

As will be obvious, the equality or inequality above discussed in termsof differential of the pulses may equally well be described in terms ofratio of the pulses.

When the detailed mode of obtaining the improvement is more closelyexamined, it becomes apparent that the basic teachings of the inventionare capable of further refinement to produce discrimination betweenaccepted pulses and rejected pulses which is even more efficient inoptimizing performance than in the case of the simple additions justdescribed. It is advantageous for ease of understanding to considerseparation of undesired pulses from signal for each particular pulse sumwithin the range of sums to be accepted. (It will be understood that sumas here used necessarily means a small but finite unit range of sums.)lf selection is approximately optimum for each individual sum, whenproperly weighted for relative counting-rate, the best possible overallratio of desired to undesired acceptance over the range of sums willresult.

In determining the optimum maximum pennitted inequality (differential,ratio, etc.) for any sum, there enter two factors of relativeprobability, first, the probability distribution or spectrum of relativepulse sizes of the coincident undesired pulses and coincident desiredpulses, respectively, which produce that particular sum as a function ofinequality, and second, the overall efficiency" of that particular sumfor the detection of desired and undesired events. The general shapes ofthe probability distributions of signal pulses and noise pulses havealready been generally discussed, and one manner of use of thisinformation described. However the same principles of selection ofcoincident pulses from the individual photomultipliers may also be usedto improve the statistical separation of pulses produced by differentisotopes and also of pulses produced by background radiation.

As will hereinafter be more fully explained, the use of the twoprobability factors mentioned to produce the closest approach to optimumcounting conditions for each sum normally produces a narrowing orreduction of the permitted differential at summed amplitudescorresponding to the highest portion of the amplitude spectrum of theisotope being counted, and the pulse-height analysis is thus desirablyperformed, for optimum results, with substantial reduction of thepermitted differential between the individual coincident pulses in theregion of the relatively infrequent maximum summed true signal pulses.

The acceptance criteria for pulses of any given sum discussed above,rather than being stated in terms of permitted inequality, may also bedescribed as varying the threshold value required for counting in eachtube (heretofore the same for all sums) in accordance with the value of,and in the same direction as, the pulse from the other tube or of thesum, and the variation (if any) of maximum permitted differential withsum may be described as the shape" of the curve (or line) of thresholdas a function of sum. From the standpoint of the general method of theinvention, such descriptions are wholly equivalent, being mere diflerences in mode of description of the concept. From the standpoint ofthe apparatus aspect of the invention, however, the implementationsuggested by such differing descriptions of the same method can resultin substantially different constructions of novel apparatus which arenevertheless closely similar in ultimate function or purpose and may beconsidered wholly equivalent as regards the broader teachings of theapparatus aspect of the invention.

As later more fully seen, the specific aspects of thepulseheight-analysis method thus far discussed may be considered, moreor less, as providing improvement on statistically selectivediscrimination against the pulses of the general character heretoforeeliminated from the count by the criteria (or apparatus) forpulse-counting acceptance generally known as coincidence threshold" andupper-level sum discrimination" in conventional window" discrimination.Further improvement, using the probability information in the individualmultiplier outputs, is obtained by substantial alteration of thecriteria for acceptance generally known as lower-level discrimination,i.e., by altering the criteria for rejection of pulses of overly smallsum. Here the difference between the shape of the equality distributioncurves of desired and undesired pulses of any given sum may be againutilized to produce improvement on the mere lower-level sum rejectionheretofore used, by incorporating the difference as an additionalcriterion of acceptance in the region of lowest amplitudes to beaccepted. Since coincident noise pulses of any given sum will have arelatively low probability of being of equal amplitude (even though farless so than at larger sum values), lower-level discrimination whichexcludes the counting of pulses of greater than a maximum differential,properly selected for each sum value, can reduce the ratio of backgroundto some degree even in sum regions so low that the peaking ofsignalpulse efficiency distribution at equality is very small. In thiscase, as later explained, a lower-level rejection criterion whichincludes a range of minimum sums, rather than a single sumlevel asheretofore, and increases the limits of accepted differential from aminimum value (or zero) at the minimum accepted amplitude sum willproduce improvement in statistical separation of signal from noise ofwhich the mere sum criterion is wholly incapable.

In addition to utility in discriminating between signal pulses and noisepulses, the relative pulse-height information of the coincident pulsesmay be employed to improve the resolution or separation of isotopes ofdifferent energies counted in separate counting channels. Heretoforesuch discrimination has likewise been performed on mere summedamplitude. in accordance with the present invention, there is no singlesum which defines the upper limit of acceptance of the lower-energyisotope or the lower limit of acceptance of the higher-energy isotope,as heretofore. Instead, the criteria for acceptance also include therelative values of the individual pulses for any given sum, and thevalue of the sum is only one of the parameters of pulse selection.

The improved analysis method of the invention, both in its generalaspects and in its more specific aspects as discussed later, may becarried out with a variety of specific apparatus. In principle, any ofthe examples mentioned above may be practiced with apparatus which is initself conventional. For example, the coincident pulse pairs from theindividual multipliers of a conventional phototube system having noassociated discrimination circuits may be used to select and rejectcounts with use of a suitably programmed computer, after digitizing theamplitudes of the pulses. Another form of known equipment which may beused is a multichannel analyzer of large capacity. Alternatively, theoutputs in the counting interval may in principle be also recorded ontape and subsequently counted in a conventional coincidence-summationsystem in a series of playbacks counting the pulses of successivelymanually set small amplitude-sum ranges, with corresponding manualincrease of the minimum coincidence-acceptance amplitude for each tubefor each successively higher range of sums, or other relativelycumbersome means employed. However, for most purposes such practice ofthe method is relatively impractical, and pulse-discrimination apparatusspecifically designed for the method aspect of the invention is providedas a further aspect of the invention, as already mentioned in the caseof addition of difference (or ratio) discrimination to prior artsystems. In a more advanced form of the invention, the sum and equalityinformation is combined and utilized in wholly interdependent fashion bygenerating a pulse signal whose amplitude is a more complex function ofthe two coincident analog signal amplitudes, selecting or rejectingcoincident pulses on the basis of the amplitude of this latter pulse ina manner generally similar to that in which sum-pulses were heretoforeemployed.

More complete understanding of the above summary, together with furtherteachings of the invention and their purpose and advantage, will beobtained by referring to the annexed drawing, in which:

FIG. 1 is a conventional representation of the pulse-height spectrum ofcarbon-l4 and background pulses in a typical summed-signal system of theprior art, showing the upperlevel and lower-level discrimination valuesemployed in forming a typical counting window;

FIG, 2 is a graphical representation of a generally similar probabilityor spectrum function for carbon-l4 and noise, respectively, for a givenvalue of the sum in the spectrum of FIG. 1, with indication of thenoise-discrimination effect of conventional coincidence-thresholdprovision;

FIG. 3 is a schematic illustration of a threedimensional coordinatesystem for representation of signal-pulse and background spectra withindividual pulses from respective photomultipliers as independentvariables;

FIG. 4 is a representation of the probability distribution of amplitudesof coincident noise pulses from the individual tubes;

FIG. 5 is a similar representation for carbon-l4 pulses, along with anexemplary noise-pulse curve;

FIG. 6 is a graphic representation of the operation of a conventionalunsummed coincidence system;

FIG. 7 is a similar representation of the operation of a conventionalsummed-pulse discrimination system;

FIG. 8 schematically illustrates the efiect of addition of a differencediscriminator on the operation shown in FIG. 7;

FIG. 9 schematically illustrates the effect of a skewed" differencediscriminator;

FIG. 10 shows, in similar representation, a manner of applying theinvention to the counting of tritium radiation;

FIGS. 11, 12, and 13 schematically illustrate various dis criminationcriteria of simple types embodying the teachings of the invention;

FIG. 14 is a generally similar plot illustrating another embodiment ofthe invention;

FIG. 15 is a graphic illustration of a manner of expressingdiscrimination criteria as functions of amplitudes;

FIG. 16 is a schematic diagram of an analog function generator forimplementing FIG. 15;

FIG. 17 is a block diagram of an overall liquid scintillation countingsystem employing the function generator of FIG. 16;

FIG. 18 is a schematic block diagram of an exemplary embodiment of theinvention as applied. to an unsummed counting system;

FIG. 19 is a schematic block diagram of a further embodiment of theinvention;

FIG. 20 is a fragmentary block diagram of another embodiment of theinvention; and

FIG. 21 is an exemplary circuit diagram of an element of the embodimentof FIG. 20.

FIG. 1 shows the conventional representation of pulseheight spectra ofbackground and scintillation pulses produced by carbon-l4 in a typicalliquid scintillation counting system, along with the counting window"formed by upper and lower discriminator levels. Such spectra have longbeen familiar to users and designers of liquid scintillation equipment,but a brief discussion of certain aspects will be useful inunderstanding the present invention.

The pulse-height spectrum of an isotope in liquid scintillation countinggenerally (but not exactly) reproduces in shape the energy spectrum ofthe emitted beta particles converted to light by the scintillationphosphor. The isotope spectrum cannot, of course, be measured directlywithout the presence of background, but the latter may be subtracted onthe basis of the background spectrum measured by use of a scintillatingsample with no emitter, and true scintillation background may beanalogously isolated from coincident noise pulses by using anoptical-only sample bottle.

It will be observed that the abscissa axis in FIG. I is indicated asX+Y. The designations X and Y are used in this and the followingdiscussion to indicate the amplitudes of the coincident pulses in theindividual tubes of a symmetrical coincidence system.

As shown by the vertical lines in FIG. 1, conventional equipment employslower and upper discrimination levels which are adjusted by the user inaccordance with the particular requirements of the measurement for whichthe equipment is being used. For gross measurements on beta-emitters ofrelatively high energy with fairly high emission rates, adjustment isfar from critical. However, as sample strength and beta-ray energy arelowered, the selection of proper levels for the windowlimits becomehighly critical in performing measurements to a desired accuracy in aminimum of time.

In the showing of FIG. 1, the ratio of the carbon-l4 pulses which fallwithin the window to the total number of disintegrations occurring inthe sample (whatever be its strength) of course constitutes theefficiency of the system for counting the isotope. Both the efficiencyand the noise are increased or decreased together by widening ornarrowing the window. The highest values of E/B, ratio of efficiency tobackground, are obtained with relatively narrow windows, selected forany particular desired count-rate. As the window-levels are moved apart,even though the increment of efficiency may bear a lower and lower ratioto the increment of background, the ratio of the square of efficiency tothe background increases until the maximum value of this ratio isreached at particular settings of the respective controls beyond whichthe ratio again diminishes.

It will be seen upon study that in essence the optimization of systemperformance is inherently obtained by employment of the principles ofstatistical probability. The graph of FIG. 1 may advantageously beconsidered as showing probability dis tribution functions of signalpulses and noise pulses, respectively, and the upper and lower leveldiscriminators may be considered as employing the sum signal informationto sort pulses on a probability basis. Pulses of a sum lying within thewindow are accepted as having a sufficient probability of being truesignal pulses and those lying outside the window are rejected as havinginsufficient probability of being true signal pulses to justifycounting. The present invention may be roughly described, in terms ofthe coordinate system of FIG. 1, as adding a third dimension to theusual pulse-height spectrum analysis, based on similar probabilitysorting using a further item of information actually contained in the Xand Y pulses, namely their relative values at any given sum.

In FIG. 2, there are illustrated the spectra or probability distributionfunctions for carbon-l4 and noise pulses, respectively, in what may bevisualized as a plane perpendicular to the drawing of FIG. 1, i.e., theprobability functions of noise and signal pulses based on relativecontribution of the individual tubes at a single value of the sumsignal, more or less analogous to a slice" taken through the plot ofFIG. 1 at the abscissa value X+Y=K. There are added, in FIG. 2, verticallines at the positive and negative values of the X-Y abscissa which havethe absolute value X+Y-T where T is the coincidence threshold, i.e., theminimum pulse from either tube which is required to register acoincidence. (It will be seen that the lowest possible value of X+Y inFIG. 1 is necessarily 2T, this being implicit in the statement that onlycoincident pulses are counted in the conventional summming system.)

As may be predicted from theoretical considerations, and as has beenexperimentally verified, where the sum signal is substantially greaterthan 2T, the probability of approximately equal noise pulses isextremely low, while the probability for carbon-l4 pulses is maximum inthe region of small differential and falls off rapidly with increasingdifferential. Accordingly, any given sum value shown as accepted in thegraph of FIG. 1 may be improved in the factor of merit by discriminatingon the basis of difference. Such discrimination is of course made,broadly stated, by the value of the coincidence threshold in aconventional system. However, the inadequacy of the coincidencethreshold setting for this purpose becomes apparent when it isconsidered how the exemplary representation of FIG. 2 varies dependenton the selection of the value of X+Y for which the probabilitydistributions are plotted. As the sum value increases, the spread ofabscissa values between the coincidence threshold limits shown in FIG. 2increases. Although the equality peak of the carbon-l4 probability curvebroadens on an absolute basis (the probability of exceeding any givendifference increasing with the sum), the peak becomes sharper as regardsisolation from the bulk of the noise pulses within the coincidencethreshold limits, and the probability of relatively equal pulsesrepresenting a signal pulse rather than a noise pulse increases more andmore with increase of the sum. Inversely, at lowermost carbon-I4 pulsesums, the curves of probability become much less sharply contrasted inshape, the ratios at zero difference being relatively small at smallsums.

With this introduction, showing generally the relationship between thepresent invention in its broadest aspects and the prior artdiscrimination methods represented by FIG. 1, explanation of a graphicrepresentation more convenient for use in further description of thepresent invention will be facilitated. As shown in FIG. 3, thepulse-height spectrum" serving as the basis for discrimination in thepresent system is conceptually best represented in three dimensions,i.e., with X and Y, the individual phototube outputs, as independentvariables generally corresponding to the sum of FIG. 1, with probabilityP being a function of these independent variables. For graphicalpracticality, however, the further graphic representations employ asingle X, Y coordinate plane, with equal probability curves" or contourlines, all points on each curve representing X and Y value contributionshaving the same probability or frequency of occurrence in thesignalpulse spectrum or noise-pulse spectrum as the case may be. Thismay best be understood from FIGS. 4 and 5, wherein there is a schematicrepresentation conveying the same general information previouslydiscussed in terms of spectra like FIG. 2 for all values ofthe sum inFIG. 1.

The form of representation here adopted is analogous to atime-integrated photograph of dots of equal intensity produced bycoincident pulses on an oscilloscope screen, each dot appearing at apoint in the plane of X and Y values determined by the amplitude of theoutput pulse from the respective tube. In such a representation of apulse-height spectrum (which may be directly produced in this fashion),there appear characteristic patterns for the pulses produced by noiseand by various isotope scintillations. The probability value in thisthree-dimensional spectrum" is represented by density of the dots at anycombination of X and Y values, and the graphic representation of eachequal-probability contour corresponds to the intersection of thesurface" spectrum with a particular probability value.

In such'graphic representations as FIGS. 4 and 5, and the furtherFigures later to be described, all points of any given X+Y value (X+Y=K)lie along a 45 diagonal line (one being shown dotted) corresponding toan abscissa axis represented in FIG. 2, the intersections of anysum-line with successive equal-probability lines representing theprobability spectrum of FIG. 2 for that particular sum. The 45 line fromthe origin (X=Y) is representative of pulse equality in the twophototubes.

The general shape of the noise spectrum is shown in FIG. 4. The greatestdensity of occurrence of the noise pulses is represented by theequal-probability curve nearest the axes, with further equal-probabilitycontours representing lesser densities or probabilities of occurrence.

The equal-probability or equal-density contours of carbonl4.are roughlyof the shape shown in FIG. 5, two being shown. As earlier discussed, theshape of the contour is basically determined by the combination of thesum spectrum of FIG. 1 with spectra like those of FIG. 2 for each of thevarious sum values. Each equal-density or equal-probability curve forcarhon-I4 is more or less in the shape of a half-oval or ellipseextending symmetrically along the 45 pulse equality line, successivelysmaller contours representing higher densities. Similar curves (notshown) for higher energy isotopes are, as may be expected from what hasalready been said, of somewhat different shape when plotted withsuitable adjustment of scale, diverging from the 45 equality line withincreasing sum value up to sum values in the region of the sumspectrumpeak rather than displaying the more or less parallel (orequal-differential) relation of the lower portions of the carbon-l4curves illustrated. This results from the fact that a conventionalspectrum like that of FIG. 1 has, in such cases, relatively few countsof small sum; for an isotope such as phosphorus-32 equal-density curvesfor very high probability values are closed loops in the region of highsum values.

It will be observed that in FIGS. 4 and 5 and certain of the furtherFigures, there appear lines parallel with, and slightly spaced from, thecoordinate axes. These lines represent the conventional coincidencethreshold for the respective tubes.

FIG. 6 portrays, in this manner of presentation, the operation of aconventional basic or nonsummed coincidence system (shown as havingsymmetry of threshold values and multiplier gains, to simplifyillustration), and FIG. 7 shows the operation of a conventional sumsystem, each showing an equal-density contour for carbon-l4 and noise.In FIG. 6, the lower and upper discriminator levels, respectively, forthe signal tube" output are shown at X, and X, and in FIG. 7 the lowerand upper levels for the sum signal are shown at Z, and Z, (thepositions illustrated not being necessarily optimum). Study of FIGS. 6and 7 will show that it is impossible to approach optimum statisticaldiscrimination between signal and noise by adjustment of discriminationlevels in these prior art systems.

In FIG. 8, there is shown in similar representation a simple addition tothe sum-system of FIG. 7 by which great improvement can be effected ineliminating noise pulses. As in FIG. 7, pulses of sum greater than Z areexcluded from counting, as are pulses of sum less than Z However, inaddition, as shown by the hatched acceptance area, there are excludedall pulses which do not lie between the lines YX=D and XY=D, i.e., allpulses having greater than a maximum permitted differential which ishere constant for all sums. Comparison of FIG. 8 with FIG. 7 will showthat such a simple addition to the conventional sum-discriminationsystem greatly reduces the noise pulses with relatively little effect onthe signal pulses.

Although the addition of discrimination on the basis of a constantmaximum permitted differential, as in FIG. h, produces substantialimprovement in the counting of carbon- 14, and can also produceimprovement for higher isotopes, any single setting of the differentialis wholly unsuitable for use with a variety of isotopes. In FIG. 9 thereis shown the operation of a skewed" differential discrimination systemadded to the conventional sum-discrimination system. Here the permittedabsolute value of the differential increases with the sum, the limits ofpermitted differential diverging with increasing sum values. Thedifferential limits are described as skewed because of the illustratedrelation to the rectangular coordinates. As shown by the legends on theskewed acceptance limits in FIG. 9, such discrimination may beaccomplished by limiting the absolute value of the resultant obtained bysubtracting a fraction k of the sum from the difference, this fractionbeing selected either by examination of contour data taken for thesystem (using the oscilloscope technique mentioned or a multichannelanalyzer), or by mere empirical experiment. As another example, aconstant voltage value C may be added to each of the phototube outputs,and the ratio of X X+C to Y+C may be generated and the pulse acceptedonly if the ratio falls between a prescribed number and its reciprocal.

By simple addition to a typical commercial liquid scintillation systemof a permanently set skewed differential discrimination circuitproducing the acceptance characteristics shown in FIG. 9, there may beachieved a large improvement in E IB (both with optimum window settingsand with settings producing higher E/B or better dual-isotopeseparation) in the counting of carbon-l4, not only without impairment ofthe performance for other isotopes, but with the realization of ameasurable improvement for other isotope energies.

The greatest performance improvement of this simple form of theinvention is obtained in the counting of carbon-l4. In the counting ofisotopes of successively higher energies, in which higher values of E /Bcan readily be obtained in an ordinary sum-window, the improvement inperformance necessarily decreases. At the other extreme, as will now beseen, the best utilization of the invention in the counting of the verylow energy radiation of tritium will usually require implementation ofthe basic method in a manner somewhat more complex than those thus fardescribed.

As was earlier indicated, the peaking of the spectrum of scintillationsignal pulses of a given sum in the region of equality, shown in FIG. 2,diminishes as smaller and smaller sum pulses are examined, thestatistical fluctuations of individual tube outputs becoming a largerand larger factor with smaller light pulses. Since the tritium spectrumhas a substantial component in the region of light intensitiesrepresenting the threshold of theoretical ability to produce oneelectron from each photocathode of most available multipliers, theindividual pulses produced by a given light intensity in this region areusually so dispersed in amplitude that the equal-density contours of theupper portion of the two-variable tritium spectrum are generally in theform of concentric circular arcs, one of which is shown in FIG. It) asthe upper limit of the hatched acceptance zone of a tritium countingsystem utilizing the invention. (The coordinate scales represented inFIG. 10 are of course greatly expanded as compared with those employedin the representation for carbon-l4). If the illustrated contour istaken to correspond with the extreme upper end of the tritium spectrum,the advantage of shaping the acceptance limit along this circular arc,as compared to any intersecting chord described by a sum-level, will beobvious in view of the high noise-pulse density at low levels. Such adiscrimination characteristic" may be obtained by analog computation ofthe sum of the squares of the individual tube outputs and comparison ofthis sum with a fixed maximum discrimination level, as indicated by thelegend in the drawing. As shown in FIG.

Hill) It), the lower discrimination limit may, as also indicated by thelegend in the drawing, be fixed by analog multiplication of the twopulse values and comparison of the product with a minimum value. In thiscase there is a range of lower-level sums in which the permittedinequality increases with the sum, while the opposite is the case in theupper-level discrimination.

It will be obvious upon study that the characteristics of FIGS. 8through are merely exemplary ofa large number of manners of obtainingimproved noise discrimination as compared with sum-discriminationsystems in accordance with the invention. In FIG. II is shown anacceptance restriction characteristic wherein the coincident pulses areexcluded from counting if either exceeds a fixed value. With a suitablyselected limit, the addition of this to the conventional sum system ofFIG. 7 will produce appreciable noise reduction for carbon-l4 counting,although less than in the case of the differential limits of FIGS. 8 and9; such a limit must not, of course, be effective in the counting of anyisotope of higher energy than that for which it is set. FIG. I3 showsthe interaction of such fixed individual limits with an upper-level sumdiscriminator. Such discrimination criteria, it will be noted, representa rough approximation to the upper-level equalprobability characteristicof tritium pulses as shown in FIG. It}, and an even closer approximationof this may be obtained by canting the individual pulse limits as shownin FIG. 112.

It will become apparent after study that exact optimization ofdiscrimination against noise on a probability basis is extremelycomplex, particularly in the region of smallest accepted sums.Theoretically, there can be defined a fully optimum boundary betweensignal pulses and noise pulses. In such a theoretical optimum boundary,the maximum permitted difference or ratio of X and 'Y pulses for everysum value would lie at the points at which either expansion orcontraction of the acceptance zone would reduce the overall factor ofmerit. Determination of the theoretical optimum pattern of divisionbetween acceptance and rejection can in principle be made for eachisotope with any given system. However, the delineating of theboundaries of the acceptance zone which is theoretically optimum for anygiven set of counting conditions is an extensive experimental task whichis not in general warranted, both because the design of readily settablediscriminator systems capable of forming complex shaped acceptance areasin the X, Y plane is difficult and because the added benefit obtained ascompared with simpler embodiments of the invention, already describedand to be later described, is relatively small, particularly when it isobserved that in practical counting, there are variables such as samplequenching, which will be mentioned later.

Thus far, the invention has been discussed primarily in connection withdiscrimination between signal pulses and noise pulses. Howeverembodiments already described are also of utility in probabilitydiscrimination between isotopes, as in the counting of dual-labelledsamples, notably with carbon-l4 and tritium. An important reason for theuse of summation of the pulses in a symmetrical coincidence arrangementin modern liquid scintillation equipment has been the belief, prior tothe present invention, that descriminationi on the basis of sum providesthe best isotope separation, i.e., the highest possible ratio of tritiumefficiency to carbon-l4 efficiency in a tritium counting channel and thehighest carbon-l4 efiiciency in a tritium-free carbon-l4 countingchannel. As shown by the present invention, this is not the case.Although sum-discrimination sharpens the energy discrimination ascompared with one-signal operation, the probability considerations whichunderlie the present invention show that substantial further improvementcan be made.

Asalready discussed in connection with FIG. Itl, equal-dew sity contourcurves for tritium in the X, Y plane are approximately circular arcs.The equal-density carbon-l4 contours in this region of very small pulses(not shown in the carbon-l4 diagrams earlier described, because of thedifference in scale) are of the same general (although not identical)shape. Under these conditions, the conventional upper tritium level sumdiscrimination (a diagonal line not shown in FIG. produces only a crudecompromise approach to optimum acceptance criteria, since the bestsum-discrimination level for approximately equal X and Y pulses ishigher than the best sum-discrimination level for very unequal pulses.If the lower discrimination level of a carbon-l4 counting channel isshaped in accordance with the equal-density contour of the tritium, itcan be given a somewhat higher efficiency for carbon- 1 4 while stillexcluding all tritium, than can be done with a mere sumleveldiscriminator. The ratio of the efficiency of the tritium countingchannel for tritium to that for carbon-l4 can also be increased somewhatby proper shaping of the upper level of this channel, as latermentioned.

The principle of improvement of isotope separation by shaping theadjoining boundaries of the discrimination characteristic or acceptancearea in the X, Y plane to appropriate curves may also be usedadvantageously in separating carbonl4 from higher'energy isotopes suchas phosphorus-32, or in any similar energy-discrimination, although theimprovement is most marked in the case of tritium and carbon. Furthersuch shaping at the top-most sum-amplitudes of even a single isotopesuch as carbon-l4 or higher-energy isotopes can produce improvement ofperformance, as now to be seen.

The improvement obtainable from shaping the upper-level discriminationcharacteristic to taper in the region of maximum pulse-heights is bestexplained by returning first to FIG. 1. The region of maximumsum-pulse-heights of carbon-14 is well beyond the amplitudes at whichthe noise having the distribution pattern earlier discussed is highlyimportant. The spectrum of total counting background, although fallingoff rapidly at low amplitudes, thereafter decreases very slowly. Thisgradually decreasing region of background, which extends to the highestbeta-induced pulse-heights, is primarily due to scintillation backgroundresulting from cosmic rays, residual radiation in materials ofconstruction, and similar sources. This radiation background may enterthe detection system in one of two ways. First, it may interact directlywith the multiplier structure, producing pulses by production ofelectron emission. Such an occurrence will here be considered as noise.The second manner of entering the detection system is by production oflight pulses in the scintillating liquid. Because of the difference ingeneral type of radiation energy, there are differences in the mechanismby which energy is converted to light, but these are not known to berelevant to the present discussion. For present purposes, the trueradiation background is considered as producing a relatively flatspectrum of scintillation intensities extending throughout the entirerange of beta-energies, an individual scintillation of any givenintensity being the same whether produced by a background event or asignal event. Discrimination against this type of background isthe'primary purpose served by the upper-level discriminator of aconventional counting window in the counting of high-energy isotopes.

Since a background scintillation of any given intensity is identicalwith a signal scintillation of the same intensity, it might at firstappear impossible to produce in the detection and counting system anychange in the ratio of signal pulses to true background pulses which isbetter than can be obtained by conventional maximum-sum discrimination.Were there exact correspondence between light-intensity and pulse-sumoutput in each scintillation event, this impossibility would in factexist; were this the case, any ratio of scintillation signal toscintillation background produced at a particular sum-value would beconstant for all values of the differential. Thus there would be no gainwhatever in ratio of signal to background by limiting the permitteddifferential whether to roughly follow an equal-probability contour orotherwise. As will now be shown, however, this ratio can actually bechanged by narrowing the permitted differential in the regioncorresponding to the top end of the spectrum of the isotope beingcounted, where the amplitude spectrum of the isotope (carbon-l4 in FIG.I) is rapidly diminishing while the amplitude spectrum of the noise isconstant or level over the same interval.

Let there first be considered the limiting case of the maximum sumamplitude of the carbon-l4 spectrum of FIG. I, i.e., the sum at whichthe counting rate becomes zero. 'lhesc pulses do not result from lightscintillations which are capable of producing this sum as the averageamplitude, but represent maximum deviations in the same direction in theoutput of both phototubes in response to the maximum-intensityscintillation in the carbon-l4 spectrum. A spectrum of carbon-I4 pulseslike that of FIG. 2 for this sum would appear as only a single pip" atthe condition of pulse equality. Accordingly, a small sum-window at thissum will include, when transposed to the X, Y plane, regions of distinctvariation in the ratio of carbon-l4 pulses to background pulses.Addition of a small maximum differential limit will produce a greatlyincreased ratio. Such a discrimination characteristic corresponds to thetip of an outer-limit (very low density) contour of the carbon-l4spectrum. In this same region of maximum sums of carbon-l4 pulses, theequal-density contours of background pulses constitute relativelyparallel lines on either side of the X=Y line.

By extension from the limiting case just discussed, it can be seen thatat any point on the signal spectrum of carbon-l 4 in FIG. I, the pulsesof the given sum which nominally correspond to a given magnitude ofscintillation intensity actually are produced by scintillations of aband of intensities. Where the frequency gradient as a function ofintensity is large, as in the latter portion of the carbon-l4 spectrumof FIG. 1, the equality spectrum typified by FIG. 2 is substantiallysharpened for any given sum as compared with the equality spectrum ofpulses produced with that same sum by light pulses of uniform intensitydistribution. Thus the narrowing of the accepted differential withincreasing sum in a manner excluding the outer comers of the hatchedacceptance area of FIG. 8 or 9 improves the ratio of acceptance ofsignal pulses to acceptance of background pulses, in addition to thesmall improvement of the noise rejection.

As will be evident, the best shaping of the acceptance characteristic inthe upper-amplitude region of the isotope to be counted does notcorrespond to an equal-density contour. Such an acceptance area would bemost desirable in any case where all events to be rejected have nodensity gradient, but constitute a uniform field in the region of theboundary. As regards noise, this condition is reasonably met, thegradient as a function of pulse inequality being small in the region ofapproximately equal pulses of sum well above the noise region." Asregards radiation background, which itself has a probability peak atpulse equality, the shaping of the upper region of accepted sumamplitudes is optimized with the acceptance limit at a substantiallyhigher value of carbon-l4 density for equal pulses than for very unequalpulses, i.e., the best discrimination curve tapers from relatively broadto very narrow differential limits much more rapidly than the isotopeequal-density curve. Accordingly, the equal-density contour is ofprimary significance for this purpose only as a general guide to theregion in which best shaping should be experimentally determined foreach type of counting problem.

From the discussion preceding, it will be seen that the shaping of theupper level of the lower-energy isotope channel in plural-isotopecounting is governed by similar general principles, the mechanism ofimprovement in the lower channel being similar. Thus in thetritium-carbon separation earlier discussed, the most desirable uppertritium boundary will be substantially flatter than the equal-densitytritium contour.

It will be observed that in the region of intermediate amplitudes, anequal-density curve of carbon-l4 has a configuration generallysuggestive of the type of differential limits shown in FIG. 8. (Theshape of the various carbon-l 4 contour curves in the regions oflowermost amplitude of course varies to a considerable degree in anyevent, but without greatly affecting this approximation of the effectproduced by employment of such a discrimination characteristic.) Asalready stated, the best constant differential limit for noisediscrimination varies with the maximum amplitude of the pulses to becounted. Accordingly, if the boundary of the discrimination area is setto correspond to the general shape of an equal-denlid sity curve, thereis achieved the noise reduction accomplished by the addition of maximumdifierential discrimination to a conventional sum system, together withthe further advantages provided by the appropriate tapering or roundingoff of the acceptance area in the region of highest magnitudes,particularly in plural'isotope counting.

In practice, as in prior art equipment, provision must be made forcontinuous variation of the discrimination level, to permit adjustmentby the user for any particular measurement. In the case of the shapedacceptance areas of the invention, the rough equivalent of the operationof variation of the discriminators of the prior art (in a horizontaldirection in FIG. I or b or inward or outward from the origin in FIG. or7) is expansion and contraction of the acceptance area by simultaneousvariation of the entire boundary. The invention in a further aspectfurther provides apparatus constructions whereby the selection ofdesired acceptance boundaries by the equipment user is accomplished in amanner generally as simple as heretofore the practice in the analogousoperation of setting upper and lower levels for counting windows.

If any given discrimination limit in the X, Y plane is approx imated asa mathematical function of the two variables, the value of this functioncan then be calculated from the X and Y outputs of each pulse andcompared with a fixed discrimination level," this comparison being madeby simple pulseheight discrimination as heretofore used on one output oron the sumpulse. The form of the carbon-l4 equal-density curves may beapproximated as a family of segments of ellipses of major axis 22 andminor axis 2W, where Z is the pulse-sum value to which the curve istangent at its tip and W is the minor axis or width" when the curve isextended to intersect with the 45 line parallel to the sum-lines andpassing through the origin. The equation of such an ellipse is:

Accordingly ellipses of related form may be constructed to have theirtip ends, at equal pulse contributions of X and Y, coincide with anygiven value of the sum. There is shown in FIG. M an acceptance area bytwo ellipses of a family wherein proportionality is maintained betweenthe parameters Z and W as Z is varied and there is shown in FIG. afamily of ellipses meeting this same equation, but with W held constantfor all values of Z.

Each of the families'of ellipses just described are related to eachother by treating Z as the sole independent parameter, with W beingproportional to Z in one case and constant in the other. Obviously, aninfinity of elliptical shapes can be obtained by varying W independentlyof Z. For purposes of utilizing the invention in its more generalaspects, which include the utilization of such ellipses in relativelycomplex methods of discrimination, the ellipse parameters may beconsidered as equally variable. (Further, it will be noted that bymoving the center point of the families along the 45 line of pulseequality, there may be obtained narrowing of the permitted differentialat low sum values, as may be felt desirable for flexibility in certaincases). However, to obtain the equipment and operational simplicityprovided by the narrower aspects of the invention, it is desirable toconsider the sole independent variable as Z, with W being consideredeither a dependent variable or a constant, in establishing the relationof a family of discrimination level" curves. In this manner it ispossible to solve the equation for Z and thus produce an expression forZ in terms of X and Y as the sole variables. Any given coincident X andY pulses may be identified as lying on the one curve of the familyhaving the corresponding value of Z. By comparison of the Z value with areference discrimination value, the pulse may be either rejected orpassed for counting.

By incorporating the expression for identification of the Z value of thecorresponding ellipse in a simple analog computer having the X and Ypulses as inputs, and the Z value pulse as the output, each pair ofcoincident pulses may be converted to a single pulse of amplitudecorresponding to the Z value and accepted or rejected by use of theusual system of upper-level and lower'level (where the lower-level islikewise to be thus shaped) pulse-height discriminators and coincidencecircuits. Comparison of the families represented by FIGS. I4 and I5 willshow that the latter provides a more satisfactory approximation to theupper contours for both carbon-l4 and tritium than the former. Byadjusting W to equal the upper-level tritium value of Z, in the case ofFIG. 115, or by making the constant unity in the case of FIG. M, therecan be obtained a circular are suitable for use as the upper-leveltritium boundary. However, when dual-isotope measurements areconsidered, it is seen that such a family as that of FIG. Ml cannot bereadily used to form both such a circular arc and at the same timeapproximate the relatively elongated elliptical shape of the uppercarbon-l4 boundary.

For the case of the constant-width ellipse family shown in FIG. IS, theequation given above has the following solution for Z:

Although the analog computation may be performed in a variety of waysknown in the computing arts, there is shown for completeness in FIG. I6a preferred construction described and explained below.

As shown in FIG. 16, the X and Y input pulses are fed to the invertinginput of an operational amplifier A producing an output pulse ofamplitude-()H-Y). The respective input resistors are indicated at R Rand the unity-gain feedback resistor is indicated at R (The stabilizingresistors connected to noninverting inputs of the operational amplifiersare omitted on the drawings.)

The X input is also connected to input resistor R of an invertingamplifier A with unity-gain feedback resistor R The output of A, isadded to the Y input, by means of respective input resistors R and R inan inverting amplifier A with unity-gain feedback resistor R to producethe pulse amplitude X Y, a balancing potentiometer R in series with Rand R producing zero output at zero difference. By means of diodes D,and D this output signal is selectively either to one input resistor IR,or the other input resistor R of the next stage. If Y is greater than X,the signal is directly fed through diode D,. If X is greater than Y, thesignal is fed to the input resistor R of an inverting amplifier A with aunity-gain feedback resistor It Thus the input signal to the next stageA is the negative of the absolute value of the amplitude difference. Thefeedback resistor IR for A is manually variable, and is employed topreset the ellipse width 2W to define the half-width W experimentallyfound to be closest to optimum for a wide range of measurements onisotopes. The interplay between multiplier gain or amplifier gain andthe computing circuit permits, in addition, expansion and contraction ofthe X and Y axes of FIG. to increase the flexibility of the system indelineating areas of acceptance in the X, Y plane. By fixing the valueof It as a fraction of the value of R or R equal to the reciprocal of W,amplifier A is made a divider producing as its output a pulse ofamplitude representative of the absolute value of the pulse differencedivided by the width W. This latter value is squared by then feeding thepulse to both inputs of a multiplier M Although illustrated as amultiplier with two inputs, M may of course be a squaring element suchas a diode of FET square if the pulses are processed at amplitudesappropriate for the range of such devices. The squared outputconstitutes one of two additively connected inputs to an in vertingamplifier A through input resistor R The second input resistor R isconnected to a constant negative 2unit reference source. The feedbacknetwork of amplifier A in addition to the unity-gain feedback resistorR,,,, includes a squaring multiplier M, so that the output of A is thesquare root of the negative of the sum of the inputs. This square rootoutput constitutes one of the inputs to a multiplier M in the feedbacknetwork of a further inverting amplifier A the input resistor to which,R is connected to transmit the (X+Y) pulse at the output of A earlierreferred to. The resistor element R of the feedback network of A isagain of unity gain value. Because the feedback of A is multiplied bythe square root value output pulse of A,, the inverting amplifier Aserves as a divider, producing at the output of the overall circuit apulse of amplitude which is the desired function of the amplitudes ofthe input pulses as set forth above.

Obviously, the analog circuits must employ amplifiers and multiplierscapable of handling the high frequencies present in the scintillationpulses to maintain individual pulse resolution, and must also introduceappropriate delays for proper synchronization. Even further flexibilitymay be added by replacing the width-adjustment potentiometer R with, forexample, a transistor or similar controlled impedance element whichdetermines the effective ellipse width W differently for each pulse bycontrolling this in accordance with, for example the value of the sumsignal, the relationship being determined by a manual control to permitmanual delineation of an essentially infinite variety of ellipselikeboundary shapes no longer restricted to any true mathematical ellipse.

It may be mentioned that the portion of the circuit of FIG. 16consisting of amplifiers A and A, through A may be used to generate theskewed difference discrimination of FIG. 9 by simple modification. Ifvariable resistance R is replaced by the standard value producing unitygain in A-,, and a fraction k of the output of A is added to the outputof A,, there results an output pulse of magnitude The feeding of thissignal to a simple pulse-height discriminator used as an anticoincidencecontrol in the same manner as an upper-level window discriminatorproduces the skewed difference discrimination which is shown in FIG. 9as an addition to a conventional pulse-height window, but is also usablealong with elliptical discrimination if so desired. It will be observedthat if such discrimination is used along with elliptical contourdiscrimination, with the ellipse of greater width than the narrowportion of the skewed differential acceptance area, the overallacceptance pattern or area will be defined by the skewed differencelines in the lower region of sums up to the point of intersection withthe ellipse corresponding to the setting of the upper-leveldiscriminator for the elliptical function and by the elliptical limitfor sum values higher than the sum value at the intersection. As in thecase of the pieced" shaping of FIGS. 12 and 13, where a plurality ofanticoincidence gating discriminators are used in parallel, theperimeter of the acceptance area will be defined by the lowest limit ofdifferential permitted by any of the superimposed boundarydiscriminators.

There is shown in FIG. 17 a schematic diagram of an overallthree-channel liquid scintillation counting system employing theinvention. The system employs the usual balanced multiplier phototubes Xand Y at 50 and 52 disposed in the counting chamber receiving the lightscintillations from the sample 54. Each of the outputs is suitablyamplified (omitted from the drawings along with the conventional delaydevices, etc.) and fed to the inputs of the usual threshold coincidencesystem, which includes discriminators fixing the usual minimum thresholdvalues. In addition, the outputs are fed to the function generator FGl,in this instance the analog computer circuit of FIG. 16, and the outputof this function generator is fed in parallel to three counting channelsA, B and C, each provided with the usual amplifying stages 58 and 60 andinterposed attenuator 62 feeding a discriminator logic system 63 thesame as that used in conventional channels, with each having a window"accepting pulses for counting only within the present limits.

The system as thus far described will be recognized as identical with aconventional summation system, with the sole exception that the functiongenerator FGI replaces the conventional pulse adder by the function ofthe two variables which identifies the ellipse corresponding to thetangent sumvalue in the X, Y plane, and thus defines an acceptance areafor each channel in which the pulses of any given sum are discriminatedon the basis of their difference as well as their sum. It will beobserved that with the lower level defined by the elliptical function,there are two symmetrical ranges of permitted differential for any givensum, equal pulses being rejected.

As can be seen in FIG. 15, the lower-level ellipse bounding theacceptance area for the lowermost channel can, by adjusting the widthcontrol of FIG. 16 to make W substantially greater than Z, be made toapproximate a straight sum-line and such discrimination may optionallybe employed for lower-level discrimination in single isotope counting.However, better discrimination against noise is obtained by utilizing aseparate function generator, shown at F62, for the lower-leveldiscrimination, One function contour for the lower-level discrimination,mentioned in connection with FIG. 10, is a constant product of theindividual pulse amplitudes. Such a function is of course far fromoptimum performance obtainable, but may be used in function generatorFG2 for simplicity of the single multiplier required. The computed valueof the function is fed to a third discriminator added to the usualcoincidence system 56, which requires a triple coincidence to pass thepulse. This function generation system effectively increases thethreshold counting value to a maximum value at the sum corresponding tothe minimum possible acceptance sum and gradually reduces the thresholdvalue required from each tube at higher sums. It is of course effectiveonly in a channel where the value of Z is eliminated as a lower-leveldiscrimination criterion by setting of the lower level of the Z windowbelow the equal-pulse threshold fixed by FG2.

Although the use of an analog function generator producing a pulsecorresponding to the value of a function of the two variables whichtakes into account their difference as well as their sum, and one ormore discriminators, gives a convenient and simple form of apparatus forutilizing the method aspect of the invention, other types ofmodification in existing equipment may be employed beyond those earlierdescribed. For example, it may be seen that from the standpoint of themethod, the delineation of maximum values of elliptical func' tions ofthe two variables may be also described as delineating a threshold valuefor each tube in accordance with the value of the pulse received fromthe other tube, or in accordance with the sum. There is shown in FIG. 18an application of the principle of the invention to an unsummedcoincidence system having only one signal tube." As here shown, thesystem includes the conventional pair of multipliers 72 and 74, eachwith a minimum level discriminator 76 and 78 constituting an input to acoincidence circuit 80 controlling the gating at 81 of the operation ofdiscrimination and counting circuits 82 of a single window system. Thesole modification of the conventional system is provision for variationof the minimum coincidence-acceptance level of the coincidence tube" 74in accordance with the value of the pulse from the signal tube 72. Wherethe modification of the coincidence threshold of the coincidence tube isa linear function of the pulse amplitude of the signal tube 72, theembodiment of FIG. 18 is in essence the incorporation of maximumdifferential discrimination in an unsummed system, and any desiredshaping can be obtained experimentally by nonlinearity of the relation.

In FIG. 19, there is shown a balanced summing system to which the typeof threshold variation just mentioned is added symmetrically. The systemis generally similar to a conventional balanced sum-discriminationsystem. However, there are added cross-connections 83 and 84 couplingthe respective signals, each to vary the threshold of the other requiredfor acceptable coincidence. As schematically illustrated, clippers 86and 88 are inserted in these couplings to render them ineffective in thelowest regions of pulse amplitude. Where the threshold variation islinear, the effect is identical with the addition of maximumdifferential discrimination to a conventional sum system. Indeed, byappropriate shaping of the variation characteristic, the upper-levelacceptance in the X, Y plane may be made to conform to elliptical orother shape. For example, if the coincidence threshold for each tube isincreased in at least the upper region of sums at a rate which increasesthe required threshold value of each tube more rapidly than half theincrease in sum, the thresholds" form a closed curve. Although such autilization of the broader aspects of the invention absorbs into thecoincidence threshold circuits the function of upper-leveldiscrimination, permitting counting of all pulses producing coincidencegating, and may be extended to inverse shaping at smallest amplitudes toreplace other forms of lower-level discrimination, it does not affordthe flexibility and convenience of the preferred forms of the inventionearlier described, but will serve as further illustration of the largevariety of ways in which the invention can be employed.

Further variations and modifications may be readily devised, Aninequality signal may, for example, be employed to vary the upper (orlower) discrimination level of a conventional summed or unsummed system,instead of (or in addition to) varying the coincidence threshold as inFIG. 19. If an inequality signal is employed to lower the upperacceptance level for the sum with increasing differential, the upper sumlevel of FIG. til or FIG. 9 becomes tapered in the general manneralready described, and the rate of taper is readily modified byattenuation of the difference signal. This corresponds to an upper limitfor the value of X+Y-k \X-Y] in the simple case of linear subtractionfrom discriminator cutoff bias.

Where great flexibility is provided to the user of equipment in theshaping of the acceptance characteristic, as in the employment ofmultiple mathematical functions in forming its boundaries, acorrespondingly great amount of experimentation is required to reachsettings appropriate for various counting conditions. Further,visualization of the meaning of the settings of the various controls interms of an overall acceptance pattern is extremely difficult.Accordingly, where extensive provision is made for pattern-shaping in acounting system of the invention, some form of visual display isnormally desirable. One such form of display is an oscilloscopepresentation of dot distribution in the X, Y plane as earlier mentioned,which may be incorporated as part of the counting system and employed toview the discrimination area (only counted pulses recorded) or theentire field (all coincident pulses recorded). Where counting rates areadequate, either pattern may be observed by mere use of along-persistence screen, but more elaborate provision may be made, suchas use of a memory tube, if the employment of photographic technique isdeemed inconvenient and counting rates are low. As a variant, probablymore readily understandable to techni cian operators, the display mayuse as the rectangular coordinates (the oscilloscope deflection inputs)the sum and difference signals, thus producing, in essence, a patternanalogous to a folding of the symmetrical X, Y plane patterns of thedrawing along the 45 line of pulse equality.

Desirably adjustments are not required to be made by the user. Theprinciples already discussed permit the design of circuits wherein thefull benefits of the invention may be automatically obtained for sampleswhich are substantially unquenched, but the advantages of the shaping atthe upper end of each isotope boundary in discriminating against scintillation background (background radiation or higher isotope) are lost forhighly quenched samples unless provision is made for restoring theregister" between the discrimination pattern and the sample spectrum inresponse to a preliminary quench correction measurement on each sample.Alteration of photomultiplier gain will to some extent restore thedesired relation, but not wholly.

lit

Substantial simplification of the adjustment requirements, manual orautomatic, can be made by employing a permanentadjustmentnoise-rejection circuit for the entire instrument range, starting justbelow the upper end of the tritium spectrum, and employing one or moreelliptical function generators, or other suitable circuits, only for theshaping of the upper (and lower where a lower-energy isotope is alsopresent) level."

A single setting for the maximum-inequality discrimination of FIG. 9which skims the extreme edge of an equal-density carbon contourrepresenting a very low counting rate is essentially universal" inimproving noiserejection for all isotopes and degrees of samplequenching. if an elliptical or analogous rejection characteristic issubstituted for mere sum discrimination in defining the upper or lowerlevel of FIG. 9, the shape of the substituted characteristic in regionsfalling outside the skew differential discriminator limits is of noconsequence. An automatic counting system designed for commercial use ofthe invention accordingly employs the acceptance characteristic of FIG.9, but is adapted for the addition of the upper and lower level shapingrefinements in one or more counting channels when these are furtherdeveloped for fully advantageous use with samples of widely varyingquench properties in an au' tomated system and has certain further noveladvantageous features.

A block diagram of this commercial system is shown fragmentarily in FIG.20, portions of the system not illustrated being essentially identicalwith corresponding portions of the diagram of HG. ll'l'. Except for theaddition of an analog computer of function generator 9%, and amodification of the coincidence logic 92 to produce an output pulse onlywhen the output of the function generator 9g is lower than a limit L(indicated by the logic legend X Y L), the diagram is that of aconventional pulse-summation system, the conventional summing for thesignal which is to be amplified and dis criminated in the respectivesignal channels being shown at 9 B. Except for the function generator90, all portions of the circuit are of the type well known.

A circuit diagram of the function generator of FIG. 20 is shown in FIG.21. The negative X and Y inputs (from a suitable preamplifier) are fedto the circuit in two paths. The first input path, through respectivecapacitors C3 and C25 and resistors R22 and R23, is to the portion ofthe circuit which produces an output pulse proportional to the absolutevalue of the difference, this being the circuit of transistors Ql3through 0H9, now to be described.

The Y pulse is amplified and appropriately stretched in duration in atwo-stage negative-feedback amplifier employing complementarytransistors one and GT7. Old is a groundedemitter PNP with the base biasfixed by resistor R37 connected to the positive supply and negativefeedback resistor RM. The collector resistor R42 is connected to thenegative supply. The second-stage NFN transistor Qi'i has its collectorresistor R 10 connected to the positive supply and its emitter resistorR 53 connected to the negative supply, its base being direcbcoupled tothe collector of @116. A high-frequency bypass capacitor C355 shunts thefeedback resistor R l-l connected between the emitter of Q17 .and thebase of Q16 to delay the pulses. The negative pulse output of theamplifier is brought out through capacitor C32 connected to thecollector of Qll7.

The amplifier for the X signal has stages OM and Q15 essentiallyidentical with the corresponding stages Q16 and 017, but with allpolarities reversed. The symmetrical complementary balance of theamplifiers is maintained throughout, the collector resistor R29 and thebase bias resistor R32 of NPN QM being of the same values as thecorresponding components of PNP Q16. Similarly, the values andconnections of the emitter resistor RM, the collector resistor R36, andthe output capacitor C30 of the PNP'transistor at Q15 are identical tothose of the NPNtransistor Q17. The feedback network R33 and C23 of thiscircuit is likewise the same, with the exception that the capacitor C23is made variable to permit adjustment of the pulse delay. The negative Xinput is not directly to the amplifier 014, an inverter stage 013 beinginserted to render the outputs subtractive. The inverter stage 013 is aPNP operated with grounded emitter and having the base and collector,respectively, connected to the junction points of bias resistor R27,feedback resistor R28 and collector resistor R31 connected between thepositive and negative supplies. The output of the unity gain inverter isthrough a capacitor C26 and a resistor R30 to the base of Q14.

The positive and negative supplies are provided with filters R44 and C31and R50 and C27 to isolate the amplifiers from the following stages. Thepositive pulse output from Q is through a capacitor C30 which isconnected to capacitor C32 to produce a difference current at thejunction. A balancing network, consisting of capacitors C29 and C37,resistors R35 and R39, and a center potentiometer R38, having its tapgrounded, is connected between the emitters of Q15 and Q17 to eliminateany residual unbalance. The circuit is balanced by adjusting R38 toproduce maximum counting-rate, i.e., minimum tripping of the limitdiscriminator inhibiting the coincidence system; in this manner anyslight unbalance of either amplifier gain or photomultiplier gain issimply compensated by utilizing the inherent properties of the system.

The net current output of the amplifiers appears at the junction ofoppositely polarized diodes CRH and CR12. When X is smaller than Y,conduction is through CR1 1, which is at the input to a currentinversion amplifier consisting of Q18 and Q19, again of complementaryconstruction. The current input is to the base of Q18, of which theemitter is grounded and the collector resistor R51 is connected to thenegative supply. The base of Q19 is direct-coupled to the collector Q18and its collector is connected to the positive supply, its emitter beingconnected to the negative supply by emitter resistor R52. The emitter ofQ19 is connected to the input at the base of Q18 through a resistor R47and a parallel stretching network R46 and C33, a small bypass capacitorC34 shunting this network. These elements, along with a resistor R45,connected to the positive supply, also fix the base bias of 018. Outputof 019 is through a resistor R48 and capacitor C39 to the emitter of asumming-circuit transistor Q20. if X is greater than Y, the in vertercircuit of 018 and Q19 is inactive, and the difference current from theX and Y amplifiers flows through CR12 and capacitor C40 to the summingcircuit input. A high-value resistor R49, connected to the negativesupply, maintains the diode CR12 at appropriate potential to equalizethe operating conditions of the oppositely connected diodes CRH andCR12.

It will thus be seen that the output of the circuit thus far describedis a multiple of the absolute difference between the X and Y pulses, thesign of the difference determining whether the output current is fedthrough capacitor C39 or C40. A diode CR14 bypasses any reverse-polaritycomponent of the input to the summing amplifier Q20.

The individual pulses from X and Y are also fed to the emitter ofsumming amplifier 020, through respective resistors R24 and R25 andrespective capacitors C4 and C12. The emitter resistor of NPN Q20, whichis operated with grounded base, is connected to the negative supply, anda small capacitor C11 shunts the emitter to ground. The collectorresistor R60 is connected to the positive supply and the collector isalso connected through a diode CR47 to a tap on the positive supply.

With this summing amplifier arrangement, the currents from the X and Yinputs and the amplified difference current produced by the inputcorresponding to the sign of the difference are added, and the desiredfunction appears as a voltage across resistor R60 which is fed to aconventional discriminator circuit (included in FIG. as part of thecoincidence logic). Each term of the function of course has a mul'tiplier determined in one case by the gain and in the other by theattenuation, in the handling of the original X and Y signals.

For the purposes later to be mentioned, an output line bearing thedifference signal (X-Y) at the junction of diodes CR1 1 and CR12 isconnected to the base of an auxiliary output amplifier Q21.

With the circuit as thus constructed, there results a discriminationsystem which does not permit counting of any coincident pulses which donot meet the requirement that the absolute value of the difference minusa constant times the sum not exceed a given limit. As will be seen fromFIG. 9, the fixing of this limit determines the minimum pulse-sum atwhich this portion of the discrimination becomes effective (generallycorresponding, in most cases, to the upper region of the tritiumspectrum) and the ratio of the gain produced for the absolute differencesignal to the attenuation produced for the sum signal at the input tothe final summing amplifier determines the slop or skewness of thedifferential limit. It is not found necessary to provide anycontrol-panel adjustments with appropriate experimental design selectionof the circuit values for any particular phototube system. The gain ofthe photomultipliers may be adjusted by the conventionally-providedadjustment of the high voltage to correct any small deviations in theeffectiveness of the system from one isotope to another, if the user sodesires.

A set of components for the circuit of FIG. 21, which has been found toproduce a high degree of improvement with any of the photomultipliertypes commonly used in liquid scintillation counting, is:

Transistors:

Ol3,0l5,Ql6,Ql8Motorola MPS6523 ()l4, Cl 7, O19, O20, O2l-MotorolaMPS652l Resistors (ohms-asterisks indicate l Diodes: lN9l6 except CRl4(979). Power supply: 12 volts, positive and negative.

With addition of the embodiment of the invention just described, it isfound that there can be achieved an improvement in the neighborhood of40 percent in the E /B ratio in the counting of carbon-l4 with ahigh-grade summation system, with lesser, but nevertheless appreciable,improvement in the counting of other isotopes. With one system, the bestobtainable ratio of the square of efiiciency (percent efficiencymultiplied by to background (in counts per minute) for carbon-l4 withoutthe improvement was 350 and, after the addition of the presentdiscrimination system, was 520, these measurements being made for awindow of 20 to 1 range at the balance point" (the point of equalefficiency gradient at each extreme of the window, commonly used tominimize the effects of small shifts).

If so desired, the auxiliary signal from transistor 021 of FIG. 21 maybe employed for the addition of further auxiliary refinements. With thecircuit illustrated, the auxiliary output signal, representing thepotential at the takeoff point, has an amplitude bearing a logarithmicrelation to the actual difference signal because of the fact that it isa characteristic of the diodes CRH and CR12 that the voltage drop is alogarithmic function of the current. For many uses, reconversion tolinearity is desirable. However, if this logarithmic signal be doubledbefore conversion, and then converted to linearity, the resultantamplitude will be the square of the difference, which may thereupon beemployed in the generation of an elliptical characteristic in any one ormore of the individual energy channels, which already have the sumsignal and thus may be readily modified for this purpose. Obviously, asimilar takeoff can be made linearly if desired, by suitable redesign.

The comparison of the individual amplitudes to distinguish, on aprobability basis, between events producing pulses of the same sum,which is the essence of the invention in its broader aspects, can alsobe advantageously employed in connection with quench correction. A knownimperfection of present quench correction measurements lies in theinability to distinguish between quenching effects produced by varioustypes of internal properties of the sample. The accuracy of the mostconvenient present quench correction measurements relies on the user'sknowledge of the factors producing the quench. The relative pulse-heightinformation may be seen to be usable in establishing such distinction.Certain forms of quenching, for example, may affect only the intensityof the emitter light, by absorbing the beta-ray energy, withoutproducing substantial attenuation of the light produced. On the otherhand, another form of quenching is mere unclarity of the fluid,attenuating the light. It will be seen-that scintillations occurringnear the wall of a sample-bottle should produce, for any given sum, asubstantially different probability distribution like that of FIG. 2 forone type of quench than for the other. In the case of thelight-attenuation, the effect of quenching will be to flatten the peakat equality, and indeed (to take an extreme example for explanatorypurposes) may produce separate peaks at sym' metrical values ofinequality. By adding to a counting system with a quench correction aprovision for measuring such shifts in the equality spectrum,statistical isolation may be produced between quenching produced by onecause and quenching produced by another. This may of course beimplemented in a large variety of ways. As one example, there may beadded to any system a provision for separately counting the pulses whichfall within and without particular differential limits. The ratio of thechannels thus formed, and its relation to the gross quench, may beemployed to identify, by usual calibra tion procedure, the type ofquench producing the spectrum shift shown by, for example, aconventional channels ratio" quench measurement. The conventional quenchmeasurement may thus be calibrated, by use of known samples, in terms ofthe quench correction indicated for the particular type (or types) ofquenching indicated by the equal-unequal" ratio, rather than employingonly a cause-independent universal" quench correction with samples ofunknown or mixed quench effects. In brief, the required quenchcorrection may be more accurately indicated by a combination of the twomeasurements than by the present quench correction measurement alone.With the same general effect, the counting rate within a narrowdifferential limit at equality may be compared with the overall countingrate for identification of the quench type, or other variants may beemployed.

Obviously, utilization of the invention is not limited to the two-tubecoincidence systems now universally used, but can be employed with morethan two tubes if and when it is desired to build systems employing morethan two tubes for forming coincidences, as has long been an obviousmanner of noise reduction. Indeed, the present invention greatlyincreases the noise-discrimination benefits obtained by adding furthercoincidence tubes. Prior to the present invention, the benefits ofhaving a third coincidence tube were severely limited by the occurrenceof what may be termed false" coincidental noise pulses actually havingthe pulse in one tube caused by a noise event in the other. The additionof a further coincidence tube heretofore gained nothing as regards suchpulses. With the relative value discrimination of the invention, thebulk of such pulses is eliminated from the count in any event, and itbecomes possible to utilize the theoretical advantages of addition of afurther tube in eliminating coincidences arising from truly random noisepulses in each tube, thus enabling major increase in the tritium-tonoiseratio.

Many other uses for the information contained in the equalitydistribution of pulses of any given sum or range of sums, concerningidentification or more exact identification of the nature of the eventscounted, will be found as the teachings of the invention are hereafterutilized in various forms. Accordingly, the scope of the inventionshould be in no way limited by the particular embodiments hereinillustrated and described, or the manner in which they are presentlyused.

What is claimed is:

l. in the method of radioactivity measurement which comprises:

a. exposing a plurality of photomultipliers to scintillations producedin response to the activity under measurement to produce a plurality ofpulse outputs, and

b. selectively processing the pulse outputs to produce measurementindications representative of coincident pulses of predeterminedamplitude characteristics,

the improvement in the selective processing characterized c.discriminating on a probability basis between pulses caused by differingevents by accepting and rejecting coincident pulses of any given sum inaccordance with the relative contribution of the individual pulses tothe sum, the minimum individual pulse required for acceptance of pulsesof some sums being substantially greater than the minimum individualpulse required for the acceptance of pulses ofother sums.

2. The method of claim it wherein only pulses of a predetermined minimumdegree of equality are accepted, to dis criminate against noise.

3. The method of claim 2 wherein the minimum degree of pulse equalityfor each sum, over a range of sums, is selected to maintain the ratio ofthe relative probabilities for the differing events generally constantover the range.

4. The method of claim l wherein the differing events are beta emissionsof different isotopes.

5. The method of claim ll wherein one of the differing events is thebeta emission of tritium, and pulses are accepted or rejected generallyin accordance with relation of the sum of the squares of the amplitudesof the pulses to a particular value.

6. The method of claim ll wherein one of the differing events is thebeta emission of carbonl4, and pulses are accepted or rejected inaccordance with the relation of an elliptical function of the pulsevalues as independent variables to a predetermined value.

7. The method of claim l wherein over a range of sums to be counted, theminimum individual pulse required for ac ceptance continuously increaseswith increasing sum.

ll. in liquid scintillation counting apparatus comprising a chamberadapted to receive a sample to be measured, first and secondphotomultipliers responsive to scintillations occurring in the chamberand producing electrical signal pulses having an amplitude distributiongenerally corresponding to the ener gy distribution of saidscintillations, and means coupled to said photoelectric devices forproviding a measurement count characteristic of the sample, includingdiscriminating means establishing a minimum limit for the amplitude ofthe pulse from each photomultiplier required for the counting ofcoincident pulses, the improvement wherein the value of the minimumlimit for the pulses from at least one photomultiplier varies with, andin the same direction as, the amplitude of the coincident pulses fromanother photomultiplier over a substantial range of amplitudes.

9. The apparatus of claim 8 wherein the discriminating means includesmeans for summing the coincident pulses and means for limiting thepermitted difference of pulses of any given sum.

10. The apparatus of claim 8 wherein the discriminating means includesmeans for subtracting the values of the pulses.

11. The apparatus of claim 9 wherein the limit of permitted differenceis the same for a substantial range of sums.

12. The apparatus of claim 9 wherein the limit of difference is anincreasing function of the sum.

13. The apparatus of claim 9 wherein the permitted difference diminisheswith increasing value of the sum over a range of sums beyond which allpulses are rejected.

14. The apparatus of claim 9 wherein the minimum limit varies with, andin the same direction as, the sum over a range of upper sums and varieswith, but opposite to, the sum in a lowermost region of sums.

15. The apparatus of claim 9 wherein the discriminating means includesmeans for establishing a discrimination limit having a maximum sum valuewhen the pulses are equal, and having limits of difference for lower sumvalues satisfying the equation where X and Y are the individual pulseamplitudes, Z is the value of the sum when the pulses are equal, and Wis a selected constant.

16. The apparatus of claim having means to vary and select the values ofZ and W.

17. The apparatus of claim 16 wherein the discriminating means includean analog computer having the individual pulses as inputs and producingtherefrom an output pulse identifying the value of Z, and amplitudediscrimination means receiving the output pulse.

18. The apparatus of claim 9 including an analog function generatorhaving the individual pulses as inputs and producing an output pulsewhich is a function of both the sum and the relative values of theindividual pulses.

19. The apparatus of claim 18 wherein the output pulse is of anamplitude which is a function of the sum and the absolute value of thedifference of the input pulses.

20. In apparatus for scintillation counting including a. a plurality ofphotomultipliers exposed to the scintillations to be counted and b.pulse-height analysis means to select coincident pulses for counting inaccordance with amplitude characteristics including means to reject allpulses below a predetermined amplitude from each photomultiplier,

the improvement wherein the analysis means further comprises:

c. means to compare the amplitudes of coincident pulses from therespective multipliers which are above the predetermined amplitude andd. means to select and reject coincident pulses for counting at leastpartially in response to such comparison.

21. The apparatus of claim 20 wherein the comparing means includes meansto produce pulses of amplitude representative of the inequality.

22. The apparatus of claim 21 further including means to additivelycombine the coincident pulses to produce pulses of amplitudeproportional to the sum, means to combine the sum and inequality pulsesto produce pulses of amplitude which is a function of boththe sum andthe inequality, and means to select pulses for counting in accordancewith the last-said amplitude.

23. The apparatus of claim 22 wherein the last-said amplitude isproportional to l x-Yl-k x+v where x and Y are the individual pulseamplitudes and k is a fraction.

24. The apparatus of claim 20 wherein the inequality pulseproducingmeans includes means to subtractively combine the coincident pulses toproduce pulses of amplitude proportional to the difference.

25. The apparatus of claim 24 including means to reverse the polarity ofonly one of the pulses, and generally identical means for amplifyingeach of the pulses and feeding them to a common output in opposedpolarity.

26. The apparatus of claim 25 having only one such com mon output, andhaving oppositely poled rectifier means coupling the common output to afurther output through respective parallel paths, only one of such pathsincluding polarity inversion means, so that the pulse at the saidfurther output is always of the same polarity and is of amplitudeproportional to the absolute value of the difference.

27. The apparatus of claim 26 having means to additively combine eachpulse appearing at the further output with at least one pulse signal ofopposite polarity aggregately proportional to the sum of thecorresponding coincident multiplier pulses, to produce a pulse ofamplitude proportional to where X and Y are the individual multiplierpulse amplitudes and k is a fraction.

28. The apparatus of claim 20 wherein the means to select and rejectpulses at least partially in response to the comparison is responsiveonly to coincident pulses of which at least one is substantially inexcess of said predetermined amplitude, so that counting of coincidentpulses all of small amplitude is unaffected.

29. The apparatus of claim 28 including means to reject coincidentpulses of greater than a predetermined total amplitude when theinequality of individual amplitudes exceeds a predetermined level.

30. The apparatus of claim 29 wherein the predetermined level ofinequality varies with the total amplitude.

31. Tl-le apparatus of claim 30 wherein the variation is linear, andhaving means independent of the comparing means for rejecting pulses ofa sum beyond selectable upper and lower levels, so that discriminationagainst noise pulses may be optimized for any selected region ofscintillation intensities by adjustment of photomultiplier gain.

1. In the method of radioactivity measurement which comprises: a.exposing a plurality of photomultipliers to scintillations produced inresponse to the activity under measurement to produce a plurality ofpulse outputs, and b. selectively processing the pulse outputs toproduce measurement indications representative of coincident pulses ofpredetermined amplitude characteristics, the improvement in theselective processing characterized by: c. discriminating on aprobability basis between pulses caused by differing events by acceptingand rejecting coincident pulses of any given sum in accordance with therelative contribution of the individual pulses to the sum, the minimumindividual pulse required for acceptance of pulses of some sums beingsubstantially greater than the minimum individual pulse required for theacceptance of pulses of other sums.
 2. The method of claim 1 whereinonly pulses of a predetermined minimum degree of equality are accepted,to discriminate against noise.
 3. The method of claim 2 wherein theminimum degree of pulse equality for each sum, over a range of sums, isselected to maintain the ratio of the relative probabilities for thediffering events generally constant over the range.
 4. The method ofclaim 1 wherein the differing events are beta emissions of differentisotopes.
 5. The method of claim 1 wherein one of the differing eventsis the beta emission of tritium, and pulses are accepted or rejectedgenerally in accordance with relation of the sum of the squares of theamplitudes of the pulses to a particular value.
 6. The method of claim 1wherein one of the differing events is the beta emission of carbon-14,and pulses are accepted or rejected in accordance with the relation ofan elliptical function of the pulse values as independent variables to apredetermined value.
 7. The method of claim 1 wherein over a range ofsums to be counted, the minimum individual pulse required for acceptancecontinuously increases with increasing sum.
 8. In liquid scintillationcounting apparatus comprising a chamber adapted to receive a sample tobe measured, first and second photomultipliers responsive toscintillations occurring in the chamber and producing electrical signalpulses having an amplitude distribution generally corresponding to theenergy distribution of said scintillations, and means coupled to saidphotoelectric devices for providing a measurement count characteristicof the sample, including discriminating means establishing a minimumliMit for the amplitude of the pulse from each photomultiplier requiredfor the counting of coincident pulses, the improvement wherein the valueof the minimum limit for the pulses from at least one photomultipliervaries with, and in the same direction as, the amplitude of thecoincident pulses from another photomultiplier over a substantial rangeof amplitudes.
 9. The apparatus of claim 8 wherein the discriminatingmeans includes means for summing the coincident pulses and means forlimiting the permitted difference of pulses of any given sum.
 10. Theapparatus of claim 8 wherein the discriminating means includes means forsubtracting the values of the pulses.
 11. The apparatus of claim 9wherein the limit of permitted difference is the same for a substantialrange of sums.
 12. The apparatus of claim 9 wherein the limit ofdifference is an increasing function of the sum.
 13. The apparatus ofclaim 9 wherein the permitted difference diminishes with increasingvalue of the sum over a range of sums beyond which all pulses arerejected.
 14. The apparatus of claim 9 wherein the minimum limit varieswith, and in the same direction as, the sum over a range of upper sumsand varies with, but opposite to, the sum in a lowermost region of sums.15. The apparatus of claim 9 wherein the discriminating means includesmeans for establishing a discrimination limit having a maximum sum valuewhen the pulses are equal, and having limits of difference for lower sumvalues satisfying the equation where X and Y are the individual pulseamplitudes, Z is the value of the sum when the pulses are equal, and Wis a selected constant.
 16. The apparatus of claim 15 having means tovary and select the values of Z and W.
 17. The apparatus of claim 16wherein the discriminating means include an analog computer having theindividual pulses as inputs and producing therefrom an output pulseidentifying the value of Z, and amplitude discrimination means receivingthe output pulse.
 18. The apparatus of claim 9 including an analogfunction generator having the individual pulses as inputs and producingan output pulse which is a function of both the sum and the relativevalues of the individual pulses.
 19. The apparatus of claim 18 whereinthe output pulse is of an amplitude which is a function of the sum andthe absolute value of the difference of the input pulses.
 20. Inapparatus for scintillation counting including a. a plurality ofphotomultipliers exposed to the scintillations to be counted and b.pulse-height analysis means to select coincident pulses for counting inaccordance with amplitude characteristics including means to reject allpulses below a predetermined amplitude from each photomultiplier, theimprovement wherein the analysis means further comprises: c. means tocompare the amplitudes of coincident pulses from the respectivemultipliers which are above the predetermined amplitude and d. means toselect and reject coincident pulses for counting at least partially inresponse to such comparison.
 21. The apparatus of claim 20 wherein thecomparing means includes means to produce pulses of amplituderepresentative of the inequality.
 22. The apparatus of claim 21 furtherincluding means to additively combine the coincident pulses to producepulses of amplitude proportional to the sum, means to combine the sumand inequality pulses to produce pulses of amplitude which is a functionof both the sum and the inequality, and means to select pulses forcounting in accordance with the last-said amplitude.
 23. The apparatusof claim 22 wherein the last-said amplitude is proportional to x- Y -k(X+ Y) where X and Y are the individual pulse amplitudes and k is afraction.
 24. The apparatus of claim 20 wherein the inequalitypulse-producing means includes means to subtractively combine thecoincident pulses to produce pulses of amplitude proportioNal to thedifference.
 25. The apparatus of claim 24 including means to reverse thepolarity of only one of the pulses, and generally identical means foramplifying each of the pulses and feeding them to a common output inopposed polarity.
 26. The apparatus of claim 25 having only one suchcommon output, and having oppositely poled rectifier means coupling thecommon output to a further output through respective parallel paths,only one of such paths including polarity inversion means, so that thepulse at the said further output is always of the same polarity and isof amplitude proportional to the absolute value of the difference. 27.The apparatus of claim 26 having means to additively combine each pulseappearing at the further output with at least one pulse signal ofopposite polarity aggregately proportional to the sum of thecorresponding coincident multiplier pulses, to produce a pulse ofamplitude proportional to X- Y -k (X+ Y) where X and Y are theindividual multiplier pulse amplitudes and k is a fraction.
 28. Theapparatus of claim 20 wherein the means to select and reject pulses atleast partially in response to the comparison is responsive only tocoincident pulses of which at least one is substantially in excess ofsaid predetermined amplitude, so that counting of coincident pulses allof small amplitude is unaffected.
 29. The apparatus of claim 28including means to reject coincident pulses of greater than apredetermined total amplitude when the inequality of individualamplitudes exceeds a predetermined level.
 30. The apparatus of claim 29wherein the predetermined level of inequality varies with the totalamplitude.
 31. THe apparatus of claim 30 wherein the variation islinear, and having means independent of the comparing means forrejecting pulses of a sum beyond selectable upper and lower levels, sothat discrimination against noise pulses may be optimized for anyselected region of scintillation intensities by adjustment ofphotomultiplier gain.